Simulation of the Matrix Bingham-von Mises-Fisher Distribution, With Applications to Multivariate and Relational Data
Simulation of the Matrix Bingham-von Mises-Fisher Distribution, With Applications to Multivariate and Relational Data
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DOI：
10.1198/jcgs.2009.07177
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发表时间：
2009-06-01
影响因子：
2.4
通讯作者：
Hoff, Peter D.
中科院分区：
文献类型：
--
作者：
Hoff, Peter D.
正交矩阵在降秩矩阵逼近和矩阵值数据分析中起着重要的作用。矩阵宾汉-冯-米塞斯-费舍尔分布（英语：Matrix Bingham-von Mises-Fisher distribution）是一种在对数密度中包含线性和二次项的正交矩阵集合上的概率分布，并在多变量和相关数据的潜在因子模型中作为后验分布出现。本文介绍了拒绝和吉布斯抽样算法从这个家庭的分布，并说明了它们的使用在蛋白质相互作用网络的分析。在线提供补充材料，包括生成本文中所有数值结果的代码和数据。
Orthonormal matrices play an important role in reduced-rank matrix approximations and the analysis of matrix-valued data. A matrix Bingham-von Mises-Fisher distribution is a probability distribution on the set of orthonormal matrices that includes linear and quadratic terms in the log-density, and arises as a posterior distribution in latent factor models for multivariate and relational data. This article describes rejection and Gibbs sampling algorithms for sampling from this family of distributions, and illustrates their use in the analysis of a protein-protein interaction network. Supplemental materials, including code and data to generate all of the numerical results in this article, are available online.